Physical law and the quest for mathematical understanding

The theoretical physics of the first quarter of the twentieth century -centering around relativity theory and nonrelativistic quantum mechanics-has had a broad influence mathematically. The main achievement of theoretical physics in the following half-century was the development of quantum field theory or QFT. Yet the mathematical influence of QFT still belongs largely to the 21st century, because its mathematical foundations are still not well-understood

Open Strings On The Rindler Horizon

It has been proposed that a certain Z_N orbifold, analytically continued in N, can be used to describe the thermodynamics of Rindler space in string theory. In this paper, we attempt to implement this idea for the open-string sector. The most interesting result is that, although the orbifold is tachyonic for positive integer N, the tachyon seems to disappear after analytic continuation to the region that is appropriate for computing ${\mathrm {Tr}} \rho^{\mathcal N}$, where $\rho$ is the density matrix of Rindler space and Re $\mathcal N$>1. Analytic continuation of the full orbifold conformal field theory remains a challenge, but we find some evidence that if such analytic continuation is possible, the resulting theory is a logarithmic conformal field theory, necessarily nonunitary.Comment: 26 pp. Comment on dilaton tadpoles in higher order added in v. 3, minor correction

Black holes and quark confinement

MOST expositions of string theory focus on its possible use as a framework for unifying the forces of nature. But I will take a different tack in this article. Rather than the unification of the forces, I will here describe what one might call the unification of the ideas

The Problem Of Gauge Theory

I sketch what it is supposed to mean to quantize gauge theory, and how this can be made more concrete in perturbation theory and also by starting with a finite-dimensional lattice approximation. Based on real experiments and computer simulations, quantum gauge theory in four dimensions is believed to have a mass gap. This is one of the most fundamental facts that makes the Universe the way it is. This article is the written form of a lecture presented at the conference "Geometric Analysis: Past and Future" (Harvard University, August 27-September 1, 2008), in honor of the 60th birthday of S.-T. Yau

Parity Invariance For Strings In Twistor Space

Topological string theory with twistor space as the target makes visible some otherwise difficult to see properties of perturbative Yang-Mills theory. But left-right symmetry, which is obvious in the standard formalism, is highly unclear from this point of view. Here we prove that tree diagrams computed from connected $D$-instanton configurations are parity-symmetric. The main point in the proof also works for loop diagrams.Comment: 18 p